When the rate of the reaction 2NO+O2=2NO2 was studied, the rate was found to double when the O2 concentration alone was doubled but to quadruple when the NO concentration alone was doubled. Which of the following mechanisms accounts for these observations?
a.) Step 1: NO + O2=NO3 (and its reverse)
Step 2 (slow): NO+NO3=NO2+NO2
b.) Step 1 (slow): NO+NO=N2O2
Step 2: O2+N2O2=N2O4
Step 3: N2O4=NO2+NO2
I thought that the rate law for the overall reaction was R=k[NO]^2[O2] but that doesn't match either of the slow reaction steps. Thanks.
To determine which of the given mechanisms accounts for the observed rate behavior, we need to analyze the stoichiometry of the slow reaction steps and match it with the experimentally determined rate law.
Let's start by examining the rate law for the overall reaction:
R = k[NO]^2[O2]
Now, let's consider each mechanism individually and check if it is consistent with the given rate law.
a.) Mechanism:
Step 1: NO + O2 ⟶ NO3 (and its reverse)
Step 2 (slow): NO + NO3 ⟶ NO2 + NO2
In this mechanism, the slow step involves the reaction between NO and NO3. However, the rate law for this mechanism should be proportional to the concentrations of the reactants involved in the slow step, which are NO and NO3. The rate law would be something like:
R = k1[NO][NO3]
This rate law does not match the observed rate law R = k[NO]^2[O2]. Therefore, mechanism a) is not consistent with the observed rate behavior.
b.) Mechanism:
Step 1 (slow): NO + NO ⟶ N2O2
Step 2: O2 + N2O2 ⟶ N2O4
Step 3: N2O4 ⟶ NO2 + NO2
In this mechanism, the slow step involves the reaction between NO and NO, producing N2O2. Checking the rate law for this mechanism, we see that it matches the observed rate law R = k[NO]^2[O2]. The rate-determining step involves the square of the NO concentration, which explains why the rate quadruples when the NO concentration doubles. The rate law also includes the concentration of O2, so when the O2 concentration is doubled, the rate doubles.
Therefore, mechanism b) is consistent with the observed rate behavior and accounts for the observations.
In conclusion, mechanism b) (Step 1: NO + NO ⟶ N2O2) accounts for the observed rate behavior where the rate doubles with the doubling of O2 concentration and quadruples with the doubling of the NO concentration.